Square root of 1652

The square root of 1652 is 40.644803 (rounded to 6 decimal places). In simplest radical form it is 2√413.

Square root of 1652

Pick any whole number from 1 to 10,000.

\sqrt{1652} = 2\sqrt{413} \approx 40.644803

How to work it out

1
The square root of 1652 is the number that multiplied by itself gives 1652.
2
1652 is between the perfect squares 40² = 1600 and 41² = 1681, so its square root is between 40 and 41.
3
Pull out the biggest square factor: 1652 = 4 × 413, so
$\sqrt{1652} = \sqrt{4 \times 413} = 2\sqrt{413}$
4
A calculator, or long division of digits, gives
$\sqrt{1652} \approx 40.644803$

LaTeX source of the formulas on this page

\[ \sqrt{1652} = 2\sqrt{413} \approx 40.644803 \]
\[ \sqrt{1652} = \sqrt{4 \times 413} = 2\sqrt{413} \]
\[ \sqrt{1652} \approx 40.644803 \]

What is the square root of 1652?

The square root of 1652 is 40.644803 (rounded to 6 decimal places). In simplest radical form it is 2√413.

Is 1652 a perfect square?

No. It lies between 40² = 1600 and 41² = 1681.

What is 1652 squared?

1652 × 1652 = 2729104.

What is the square root of 1652 rounded to 2 decimals?

40.64.